What is happening to Suzanne's eyes during this use of the Boolean modifier?
You are using a non manifold mesh. Basicly, non manifold means, in layman's terms, not water tight. 

Here is an example:



The cube has a hole in it. In Suzanne's case, its the fact that her eyes aren't attached to her head.

Here is a quick way to fix Suzanne:



Note: I use the loop tools add-on accessed by W